Answer
$a.\displaystyle \quad f^{-1}(x)=\frac{1}{m}x$
$ b.\quad$The graph of $f^{-1}$ is a line through the origin with reciprocal slope ($\displaystyle \frac{1}{m}$).
Work Step by Step
$ a.\quad$
Set $y=f(x)$. Interchange x and y
$y=mx$
$x=my$
... solve for y
$y=\displaystyle \frac{1}{m}x$
... replace y with $f^{-1}(x)$
$f^{-1}(x)=\displaystyle \frac{1}{m}x$
$ b.\quad$
Note that the original line passes through the origin and has slope $m.$
The graph of the inverse function is a line through the origin, with slope $\displaystyle \frac{1}{m}$.
In other words, the graph is a line through the origin with reciprocal slope.
